Given $ m \angle QPR = 7x + 146$, $ m \angle RPS = 2x + 14$, and $ m \angle QPS = 169$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Explanation: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {7x + 146} + {2x + 14} = {169}$ Combine like terms: $ 9x + 160 = 169$ Subtract $160$ from both sides: $ 9x = 9$ Divide both sides by $9$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 7({1}) + 146$ Simplify: $ {m\angle QPR = 7 + 146}$ So ${m\angle QPR = 153}$.